expand the expression to a polynomial in standard form

Question

(x-9)(x^2+x+2)
you made me get the other question wrong so dont make me fail

Answer 1

To expand the expression \((x - 9)(x^2 + x + 2)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(x\) to each term in \(x^2 + x + 2\): \[ x \cdot x^2 = x^3 \] \[ x \cdot x = x^2 \] \[ x \cdot 2 = 2x \]

   So, the result of distributing \(x\) is: \[ x^3 + x^2 + 2x \]

2. Now, distribute \(-9\) to each term in \(x^2 + x + 2\): \[ -9 \cdot x^2 = -9x^2 \] \[ -9 \cdot x = -9x \] \[ -9 \cdot 2 = -18 \]

   So, the result of distributing \(-9\) is: \[ -9x^2 - 9x - 18 \]

3. Now, combine all the terms from both distributions: \[ x^3 + x^2 + 2x - 9x^2 - 9x - 18 \]

4. Combine like terms:

   • \(x^2 - 9x^2 = -8x^2\)
   • \(2x - 9x = -7x\)

So the expression simplifies to: \[ x^3 - 8x^2 - 7x - 18 \]

Thus, the expanded expression in standard form is: \[ \boxed{x^3 - 8x^2 - 7x - 18} \]